Current is moving charge, typically electrons. And just as the amount of water flowing in a river can be measured, so can the amount of flowing electrons through a medium. To make this measurement, we simply pick a reference point and count the number of electrons that flow past that point over time.
The standard measure of electrical current is the Ampere, often referred to just as “amp”. It is equal to 6.24e18 (that’s 6 quintillion!) electrons flowing past a reference point in 1 second. The amp is named after André-Marie Ampère, a French physicist credited with the discovery of electromagnetism.
Many times the term amp is abbreviated as just a capital A. For example, instead of seeing “5 amps” it may be more common to see “5A". This is especially true when SI prefixes are used, such as writing 5mA instead of 5 milliamps.
Finally, the terminology of current is often abbreviated with the letter I (probably because the letter C had already been used as an abbreviation for charge). Electrical schematics that need to show the presence of current in a portion of a circuit will often use the letter I as a symbol for current.