Proliferate (CR 701.27) lets you choose any number of permanents and/or players that already have counters on them, then put one additional counter of each kind that permanent already has on it. Loyalty counters are a type of counter like any other, so a planeswalker with at least one loyalty counter on it is a legal target for proliferate.
The key requirement is that the planeswalker must already have at least one loyalty counter on it. A planeswalker that has somehow lost all its loyalty counters (and survived via a replacement effect) would have no counters to proliferate. Under normal circumstances, every planeswalker on the battlefield has at least one loyalty counter, so this is rarely an issue.
When you proliferate, you add exactly one loyalty counter per planeswalker you select. This effectively gives that planeswalker +1 loyalty without needing to activate an ability, and it counts as a counter being added, not a loyalty ability being activated.
Concrete example: You control a Jace, the Mind Sculptor with 3 loyalty counters. You cast Karn's Bastion and activate its proliferate ability. You choose Jace — he now has 4 loyalty counters, moving him one step closer to his ultimate without spending an activation.
Relevant rules: CR 701.27 (Proliferate), CR 306.5b (loyalty counters on planeswalkers), CR 122.1 (counters defined).
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.