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It's hard to answer your question specifically without the context, and obviously the physical significance of some expression depends on what the variables and operations in that expression stand for. Before considering this particular integral, I want to talk about integration generally and its notation.
When we integrate some function, we integrate it over a domain, usually some submanifold of some enclosing [manifold](https://en.wikipedia.org/wiki/Manifold), often $\mathbb R^n$. If we have some function $f : \mathcal M \to \mathbb R$ defined on some manifold $\mathcal M$, then we could write $\int_{\mathcal N} f(x)\mathrm dx$ for the integral of $f$ over the domain $\mathcal N$ where $\mathcal N$ is a submanifold of $\mathcal M$. For our purposes here, you don't need a super precise understanding of what a manifold is. The vague notion that it's some kind of reasonable shape like a plane or a torus is fine. As an example, we can talk about integrating over the unit disc at the origin in the plane and might notate that as $\int_D f(x, y)\mathrm dx\mathrm dy$. This would involve integrating $f$ over all the points $(x,y)$ such that $x^2 + y^2 \leq 1$. In particular, $\int_D \mathrm dx \mathrm dy = \pi$, the area of the unit disc.
In early calculus often the notation $\int_a^b f(x)\mathrm dx$ is used. This corresponds to integrating over the closed interval $[a,b]$, i.e. $\int_a^b f(x)\mathrm dx = \int_{[a,b]} f(x)\mathrm dx$. Multiple integrals are what they say, but we do have $\int_a^b \int_c^d f(x, y)\mathrm dx \mathrm dy = \int_{[a,b]\times[c,d]} f(x, y)\mathrm dx \mathrm dy$ where $[a,b]\times[c,d]$ is the submanifold of $\mathbb R^2$ whose first component is in $[a,b]$ and whose second component is in $[c,d]$, i.e. it is a rectangular area in $\mathbb R^2$.
Given this, your original integral is presumably an integral over some unspecified (at least not in the expression) $6$-dimensional (sub)-)manifold (or potentially some dimension that's a multiple of $6$ depending on the dimensions of the variables, but I'll assume they're $1$-dimensional). We can also see that this integral will give us the (hyper-)volume of that (sub-)manifold in exactly the same way the similar integral above gave the area of the unit disc. Based on the naming of the variables, I assume this is a volume of some submanifold of the [phase space](https://en.wikipedia.org/wiki/Phase_space) probably for a simple particle. While not directly tangible, the sub-volumes of phase space and the [preservation of the volume of phase space](https://en.wikipedia.org/wiki/Liouville's_theorem_(Hamiltonian)) are extremely important facts in physical theories. For example, in the [famous formula](https://en.wikipedia.org/wiki/Boltzmann_entropy) $S = k\ln W$ for entropy, $W$, in modern interpretations, is usually viewed as the volume of the submanifold of phase space compatible with some given values of macroscopic variables.

It's hard to answer your question specifically without the context, and obviously the physical significance of some expression depends on what the variables and operations in that expression stand for. Before considering this particular integral, I want to talk about integration generally and its notation.
When we integrate some function, we integrate it over a domain, usually some submanifold of some enclosing [manifold](https://en.wikipedia.org/wiki/Manifold), often $\mathbb R^n$. If we have some function $f : \mathcal M \to \mathbb R$ defined on some manifold $\mathcal M$, then we could write $\int_{\mathcal N} f(x)\mathrm dx$ for the integral of $f$ over the domain $\mathcal N$ where $\mathcal N$ is a submanifold of $\mathcal M$. For our purposes here, you don't need a super precise understanding of what a manifold is. The vague notion that it's some kind of reasonable shape like a plane or a torus is fine. As an example, we can talk about integrating over the unit disc at the origin in the plane and might notate that as $\int_D f(x, y)\mathrm dx\mathrm dy$. This would involve integrating $f$ over all the points $(x,y)$ such that $x^2 + y^2 \leq 1$. In particular, $\int_D \mathrm dx \mathrm dy = \pi$, the area of the unit disc.
In early calculus often the notation $\int_a^b f(x)\mathrm dx$ is used. This corresponds to integrating over the closed interval $[a,b]$, i.e. $\int_a^b f(x)\mathrm dx = \int_{[a,b]} f(x)\mathrm dx$. Multiple integrals are what they say, but we do have $\int_a^b \int_c^d f(x, y)\mathrm dx \mathrm dy = \int_{[a,b]\times[c,d]} f(x, y)\mathrm dx \mathrm dy$ where $[a,b]\times[c,d]$ is the submanifold of $\mathbb R^2$ whose first component is in $[a,b]$ and whose second component is in $[c,d]$, i.e. it is a rectangular area in $\mathbb R^2$.
Given this, your original integral is presumably an integral over some unspecified (at least not in the expression) $6$-dimensional (sub-)manifold (or potentially some dimension that's a multiple of $6$ depending on the dimensions of the variables, but I'll assume they're $1$-dimensional). We can also see that this integral will give us the (hyper-)volume of that (sub-)manifold in exactly the same way the similar integral above gave the area of the unit disc. Based on the naming of the variables, I assume this is a volume of some submanifold of the [phase space](https://en.wikipedia.org/wiki/Phase_space) probably for a simple particle. While not directly tangible, the sub-volumes of phase space and the [preservation of the volume of phase space](https://en.wikipedia.org/wiki/Liouville's_theorem_(Hamiltonian)) are extremely important facts in physical theories. For example, in the [famous formula](https://en.wikipedia.org/wiki/Boltzmann_entropy) $S = k\ln W$ for entropy, $W$, in modern interpretations, is usually viewed as the volume of the submanifold of phase space compatible with some given values of macroscopic variables.

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