Some of the things which can cause train backups and stoppages and how to fix ...

(1) not enough power for a gradient - add another loco
(2) if the signal is positioned very close to the end of the stationary train in front - move the signal back a bit.
(3) power supply issues - check if you are near the limit and add more power stations.
(4) if you recently changed the route and trains are gridlocked (too many trains on a loop) .. build a siding or bypass to free it up and review train routes, might need to optimise and reroute.
(5) incorrect signalling - check if signals are flashing exclaination marks, if they are go up to them and 'E' and check the status to see the error. Also you can drive the train to see errors too.
(6) Sometimes if you've re-railed a train or had an error, you need to re-enable auto-driving.
(7) Sometimes your train route might cause weird behaviour - if in doubt, ride the route. You may find the train goes a strange way.
(8) Look out for funnels - places where lots of trains go through a single point. They look cool, so you dont have to remove them, but check the signals carefully to keep them moving.
(9) Block design. Placing block signals creates 'Blocks' or sections of track. Ensure each is just over the length of the trains that use it.
(10) Place signals just after merges or splits to split each track into its own block so the train on track A doesnt occupy the block, preventing trains moving on track B.