A few things that will help. Although the things I'm talking about here are generalized and are WAY more involved in reality than some of my over simplistic explanation, their basic understanding is important to the movie.
Special Relativity- this was one of Einstein's 1905 works that he submitted to journal while he worked at a Swiss patent office. (E=MC2 came that year as well.) Special relativity has a lot of implications. SR allows for time to be added to the three dimensions of space that we encounter intuitively in reality. (Up/down, left/righ, forward/backward) This is what is known as the spacetime continuum. Basically Einstein surmised that objects that move at different speeds through spacetime experience time differently relative to others frame of reference. In other words, if you were on the ground and someone took off in a rocket that could approach the speed of light, they would age differently relative to the person on the ground. This has been proven in countless experiments over the years. There is direct evidence to support this.
General Relativity-this was Einstein's 1916 addition to relativity. GR is a basic theory of gravity. Important to the movie is that the space around mass warps or bends. So this causes warps and bends in space-time. As a result, objects that get close to gravitational fields experience time differently as well. The closer they get to the object the slower time passes relative to objects outside of that gravitational influence. This is also something that has been supported through experimentation numerous times. In fact, our GPS satellites has to use a GR adjustment in calculation to account for the difference between gravitation on the satellites with that on the earth.
Black holes- this one is fairly easy. A black hole is a region in spacetime where the mass is so great and the gravity so powerful that not even light can escape. These can be formed after the demise of a very large star when it collapses in on itself after it is spent. These gravitational giants can suck in other black holes, stars, etc. and gain mass. In the movie, much of it takes place near a massive black hole called Gargantua. This causes unique problems with time based on the above relativity. Black holes also have been directly observed.
Event Horizon- this is the point in space surrounding a black hole that if you were to cross you would be swept in never to return.
Wormhole- this is a phenomena that is theoretically and mathematically possible but has never been directly observed. Because we know that the cosmic speed limit is the speed of light (you can't go faster), that puts the ability for man to travel to most of our universe out of reach because it would take longer than our life expectancy to get there. But because we know that large massive objects bend spacetime, it is possible for a shortcut to help us reach parts of space unreachable conventionally. Imagine a napkin is a slice of spacetime. To travel from one side to the other you would have to travel in a straight line. Now fold the napkin over (imagine this fold was done by a massive object like a black hole in space) and now you have the edged lined up next to each other. A wormhole is made theoretically possible by some gravitational force on both sides of the napkins causing a funnel to connect to two points in space. By going through that wormhole you would be in effect taking a shortcut to parts of the universe that you could never reach in a linear path. Again...this works mathematically but has never been observed.
Tesseracts- a four dimensional hyper cube. I'll find a picture and post it.
Fifth Dimension-we have two dimensions on paper. We have three dimensions in observable space. We have four dimensions when you include time. A fifth dimension is a theoretica and hypothetical construct. There is no direct observation but it is argued to exist by theoretical physicist. We normally and intuitively envision time as flowing in a straight line. Einstein showed in relativity that time was relative to the frame of reference of the observer. In a hyper dimensional space it is theorized that time might not flow linearly, but flow simultaneously. In other words your entire life...your birth, your death, everything... is happening at once. This plays an important part in the movie and is illustrated through the above tesseracts. This is the part of all of this that I have the most difficult time getting my head around because it is counterintuitive by nature.
Anyway...if you familiarize yourself with the above it will make the movie more enjoyable.