Venmo is a mobile payment service owned by PayPal. Venmo account holders can transfer funds to others via a mobile phone app; both the sender and receiver have to live in the U.S.
In order to accept Venmo payments in Gift Up! you need to attach a PayPal or Braintree account to Gift Up! (PayPal own Braintree as well) and Venmo will automatically be offered in your Gift Up! checkout if your underlying PayPal account supports it.