Smart Tap redemption is the moment a Google Wallet pass is read over NFC. Google's own term for it is redemption whether or not anything is actually redeemed: for a loyalty pass, the "redemption" is simply the reader receiving the member identifier so the point of sale can look the member up.
What is sent is the pass's Smart Tap redemption value, a string the issuer sets on the pass object when the pass is created. In a loyalty program it is usually the member ID or the same value the pass's barcode encodes, so the point of sale handles a tap and a scan identically. The value is encrypted for the merchant's reader using the Smart Tap key, and the phone only sends it to a reader whose collector ID the pass class has authorized.
Two settings gate it. Smart Tap must be enabled on the class, and the class must list the collector IDs allowed to redeem. A pass created without either shows a barcode in the wallet but does not respond to a reader, which is the first thing to check when Android members cannot tap.
At the till, Smart Tap redemption and the Apple VAS read are two halves of one NFC identification flow. A reader configured for both polls for both, the phone answers with whichever pass it holds, and the terminal passes the identifier along the same path; on payment terminals this happens inside card acquisition, so the loyalty read can share the tap with payment.
Smart Tap can also write back to the phone, for example to tell the wallet a coupon was redeemed. Most loyalty programs never use that path: the pass is updated through the Wallet API after the transaction, which keeps the terminal integration to a read.