。
I remember mother holding me tightly.
Literal
Mother [subject-が] me [obj-を] strongly held-tight [nominalizer-のを] recall.
抱きしめる is a compound verb from 抱く ('hug') + しめる ('tighten'), yielding 'hold tight' or 'embrace firmly.' のを思い出す nominalizes the preceding clause and marks it as the object of 思い出す ('recall, remember'). The structure is the standard way to say 'remember that X happened' in Japanese — 思い出す takes a nominalized clause as its object.