Detailed Answer: 

A pending donation on the PayPal Standard gateway means one of two things:
  1. Your donor was redirected to paypal.com but didn’t finalize their donation.
  2. After your donor finished their donation on PayPal.com, the donor didn’t click the “Return to {website}” link. That link would return them to your Donation Confirmation page and send a signal to Give that the donation completed. Without that signal, Give can’t know that the donation completed. On some PayPal accounts, the second issue can be mitigated by a redirect: PayPal will redirect back to the donation confirmation page on a successful donation after a number of seconds. On other, newer accounts, that’s a paid upgrade.
What you should do:

You should contact PayPal directly to ask for that option to be enabled for your business account.

Being redirected (or clicking) back to the donation confirmation page is crucial in the donation being marked as complete, since there is a slug attached to the end of the URL confirming which donation it is, etc. That slug includes what PayPal calls the IPN or “Instant Payment Notification.” Without the IPN, there’s no way for Give to “know” which payment has gone through to PayPal. If a donor doesn’t finish their donation, Give puts the donation into “Pending” status. If you cross-check with your PayPal account and notice that that donation was indeed finalized, manually change the status in Give to “Complete”. If you do not do that within around 7 days, Give will automatically change that status to “Abandoned” — meaning the donor never finalized their donation.

Note: if you find that MOST of the donations in Give that are marked as “Pending” were actually Complete in PayPal.com, then please contact the Team at Buzz and we will work with the Team at Give to troubleshoot for you.