Today is Ash Wednesday, the first day of Lent. Ash refers to ashes, the residue of wood or something that has been burnt, and is meant to symbolise human mortality.
The word 'ash' has been around in English for a long time - there is the common tree, the ash, for instance. Ash is also the name of the Old English letter, or ligature (2 letters joined together), æ (ash was written æsc at the time). This vowel was pronounced like a short a, and was commonly used in Old English words (see this old post of mine, for instance).
When the Angles and the Saxons invaded England in the 5th century they brought their runic alphabet with them. One of the runes was ᚫ, called ash because it also meant ash tree. The letter æ developed from ᚫ, so kept the same name.
Occasionally, the ligature æ is used in modern English spelling eg archæology or encyclopædia, but it is not as common as it used to be, and it is becoming even less so.