How to Unblock Someone on Gmail
You can block a contact within Gmail's Chat feature or through Hangouts. In either case, you can unblock the contact in Gmail using the Unblock option next to contacts or within a Chat window, but the changes take place only within Gmail. If you want to simultaneously unblock the contact for Gmail, Hangouts and other Google products, however, you'll need to unblock him from Hangouts' Blocked People list.
Unblocking Within Gmail
Blocked contacts don't appear in Gmail's Chat list, so enter the person's name or Google ID in the Chat panel's search field to locate the contact. Move your mouse pointer over the contact and then click "Block [Name]," which should currently be checked. Doing so immediately unblocks the contact in Gmail and allows the contact to reappear in the Chat list. If you have the contact already opened in a Chat window, you can also click the window's "More" menu and then select "Unblock [Name]."
UnBlocking Contacts Within Hangouts
Click the Hangouts list's triangular "Menu" icon and then select "Blocked People" to see a list of contacts you've blocked. Locate the contact you wish to unblock and then click "Unblock" next to the listing. The contact is then unblocked in Hangouts, Gmail and other Google products.