Short Rest
A short rest is at least 1 hour of light activity — eating, tending wounds, reading. At the end, you can spend Hit Dice to heal: roll the die, add your Constitution modifier, regain that many hit points, per die spent. You decide how many to spend.
Long Rest
A long rest is at least 8 hours — at least 6 asleep, no more than 2 hours of light activity (keeping watch counts). At the end you regain all lost hit points and recover spent Hit Dice up to half your total (minimum 1). You can't benefit from more than one long rest per 24 hours.
Interrupted Rests
A short rest is interrupted by anything more strenuous than light activity — you'd need to start over. A long rest is only ruined by 1 hour or more of strenuous activity (fighting, casting spells, marching); shorter interruptions just add their time to the rest.
Hit Dice
You have one Hit Die per character level, of your class's die type. They're your short-rest healing currency and partially refill on a long rest — managing them across the adventuring day is core 5e resource play.