In backgammon, you are trying to get your pips (your checkers) home whilst preventing the other person from doing so before you.
You run- try to get all your pips home as fast as possible
You block- make it hard for the other player to get their pips home.
You can do a combination of the two- blocking and running in response to your die rolls. Luck is a huge aspect of backgammon, so responding to your dice rolls is important.The Game is a balance of defence and attack, depending on what your opponent does and how good your dice are.
In general, you want to avoid getting put on the bar (being a blot, when you have one pip alone on a point and your opponent lands on it, meaning you have to start over with it) but sometimes, it can be strategic such as when your opponent has several blots in/ adjacent to their home court. Don't just "bump" people onto the bar without considering your own situation.
If you get stuck in your opponent's home court, you can try to run or you can hole up and wait to try to bump them.
The points- going from the one colour to the same is always an even number; going to the other colour is an odd number.
You have lots of pips in your home court to help you block it- there are some classic blocking rolls- 6/1, 3/1, 4/2, 5/3. Learn the classic moves, and it makes play easier. For example, a 5/6 gets the 1 pip in your opponents home court to the opposite end of the board.
It helps to watch your opponent- if they are running, try to block. If they are blocking, run before they trap you. It doesn't always work, but ... it's one way to approach the game.
Note- if you can play the dice two ways, but one means you cannot move one die, you can't make a move that means you lose the other move. You have to move with both dice if you can.
If both players have started to "bear off" (that means all the pips are in the home court and being removed from the board), then whoever gets all their pips out first wins a single game. If the losing player still has pips in their opponent's home court, or on the bar, it's a Backgammon (a win x 3). If the losing player has pips outside the home courts, or they are all in the home court but they haven't started to bear off, it's a Gammon (win x 2). (BGA doesn't credit you the extra wins, but it's still satisfying!)
The only way to get good is to play, play, watch how others play, and play more. A beginner can beat a Master with the right dice.