A reciprocal link is when site A links to site B and site B links back. It happens naturally between partners, integrations and sites that cover each other.
It becomes a problem when it's arranged purely for links ("I'll link to you if you link to me") and done at scale. Google lists excessive link exchanges as a link scheme.
In outreach, avoid offering a link back as payment for a link. Offer something useful to their readers instead.
Example
Margin and a citation manager it integrates with linking to each other's integration pages is natural; Margin trading links with 50 unrelated blogs is not.
Putting it into practice
Where to use it: White-hat link building checklist and Declining a paid-link request.