Patañjali's yogasūtra 1:11 Smṛitiḥ

अनुभूतविषयासंप्रमोषः स्मृतिः 

anubhūtaviṣayāsaṃpramoṣaḥ smṛitiḥ

अनुभूत विषय असंप्रमोषः स्मृतिः 

Memory is not allowing a subject which has been experienced to escape [from the mind]. 

अनुभूत - experienced; past participle from anu+√bhū i.e. that which follows [a] happening 

विषय - subject, matter, object, topic; masc. noun

असंप्रमोषः - not allowing to be carried off; masc. noun from a+sam+pra+√muṣ (1P) 

स्मृतिः - memory, remembrance; fem noun

Memory, then, is the retention of experiences in the mind. These are retained in a potential state, as impressions (saṃskāra). It is when these impressions are converted from their potential state into an active mental process that it is considered a citta-vṛitti (modification/activity of the mind).

The process by which this activation takes place is complex and not fully explicable.  But to understand it, think back to the number times have you said in frustration - "Oh, his name is on the tip of my tongue ... I can see his face but I can't remember his name!"  That is the memory in the potential state. And when it suddenly 'comes back to you' (chamkaa!!) right then or maybe after a night's sleep, or a few days later, even after you've stopped trying consciously to remember - that is when it has  become an active 'memory', a citta-vṛitti.

Yogis believe that perseverance and balanced emotion can help sharpen this process - i.e. improve your smṛitḥ, your memory. They also believe that the more good saṃskāra you have, the better a person you will be.