Let's take a look at the field equations written by Einstein:
#R_(mu nu)-1/2g_(mu nu)R+g_(mu nu)Lambda=(8pig)/(c^4)T_(mu nu)#
So, what the hell is this hot mess all about? Let's take a look term by term (ish).
#R_(mu nu)#, #g_(mu nu)# and #T_(mu nu)# are what we call tensors in math and are irrelevant right now.
The #T_(mu nu)# tensor is essentially any stress or energy (or momentum or mass) carrying medium throughout the universe - and the #g_(mu nu)# is the metric tensor (let's just ignore this mathematical jumbo for now). The #mu nu# here represent the space and time components. This energy/mass/stress/momentum medium is then multiplied by some fundamental constants of the universe and this forms the right hand side of the equation.
The basis of the field equations utilize Riemann geometry which essentially describes the curvature of smooth surfaces in higher dimensions. So, the #R_(mu nu)# describes the curvature of space and time. However, conservation of energy and momentum states that #grad^(mu)T_(mu nu)=0# as #T# stays constant (conserved). So, to balance this, we subtract #1/2g_(mu nu)# (metric tensor) and we get the Einstein tensor:
#G_(mu nu)=R_(mu nu)-1/2g_(mu nu)#
The Einstein tensor on the left hand side describes the curvature of space and time, and this is equated with energy and momentum (and mass) on the right hand side. So, mass can curve space. And curved space means gravity.
However, there is one term which we missed: #g_(mu nu)Lambda#
The #Lambda# here is the universal constant. Einstein originally introduced it here because he found that his original equation described a universe which was expanding. However, he later abandoned it calling it the "greatest blunder of his life."
Ok. There we have it. This is how (General) relativity describes the Universe.