Translation Suggestions
Suggestions allow users to propose changes to strings without editing them directly. The actual string value is changed after a reviewer approves the suggestion.
Suggestions are also how community translation works. On a public project, anyone signed in can suggest without becoming a member.
How to enable suggestions
Go to Project settings > Advanced > Suggestions mode.

How to Add Translation Suggestions
Once suggestions mode is enabled, users can edit a translation or add a suggestion.

Review and Approve Suggestions
When a translator adds a suggestion, it is visible in the translations view, but not active (meaning if translations are exported, there is still the old translation).

Once a reviewer comes along, they can accept the suggestion.

This is the moment when it will replace the existing translation.

When there are multiple suggestions on a string, you choose how accepting one affects the rest.
Accept only promotes the suggestion to the live translation and leaves the other suggestions
open, so you can keep comparing them. Accept and decline others, in the suggestion's ⋮ menu,
promotes the suggestion and dismisses the competing ones in a single step.
Tolgee shows up to three suggestions on a string at once. If there are more, use Show all to see
the rest. All previously accepted and declined suggestions are also found under Show all.

Protecting reviewed translations
Tolgee offers a mode where translators can only edit non-reviewed translations directly. You can enable this in advanced project settings:

So now, when a translator opens a reviewed translation, they can only suggest.

Granular protection
If you want more direct control over edit permissions and suggestions, you can do it through Granular permissions.
Here you can, for example, only allow the user to Suggest, so they can't edit any translation directly.

Accepting the suggestions is tied to the "Change state" permission (which is what all reviewers have).