How do I explain a gap in my employment history?
Briefly, honestly, and with the emphasis on the present rather than the past. Gaps are far more common than the anxiety around them suggests, and interviewers encounter them constantly. What creates a problem is evasiveness, not the gap itself.
A workable structure is one sentence on what happened, one on anything you did during it that is relevant, and then a return to why you are well placed for this role now. The brevity signals that you do not regard it as a problem, which is most of the battle.
Common reasons need no elaborate framing. Redundancy, particularly in a round affecting many people, is ordinary. Caring responsibilities are ordinary. Health, whether your own or a family member's, warrants no detail beyond saying it is resolved and you are ready to work; you are under no obligation to disclose medical specifics. Study, travel and deliberate breaks are straightforward. A period of job searching in a difficult market is common and better stated plainly than disguised.
On the CV itself, using years rather than months collapses short gaps without misleading anyone. A longer gap is better labelled briefly than left as an unexplained absence, since an unexplained absence invites the reader to imagine something worse.
Two things genuinely harm you. Lying, which tends to surface during reference checks and is far more damaging than the gap. And over-explaining, which signals shame and invites the interviewer to treat it as significant.
If you did anything during the period that keeps skills current, mention it once without inflating it.