IPA: /ˌʌnɪˈraɪkli/
KK: /ʌnɪˈrɑɪkli/
In a way that is sincere and without any hint of sarcasm or irony.
She said she loved the movie unironically, meaning she truly enjoyed it without any sarcasm.
Unironically → It is formed from "un-" (meaning not) and "ironically" (from Greek "eironeia", meaning dissimulation or feigned ignorance). The word "unironically" means in a manner that is not ironic, or sincerely.
Think of 'not' ('un-') being added to 'dissimulation' ('ironically') — this helps you remember that 'unironically' means to express something sincerely.