Shuffling your hand or Deck means sufficiently randomizing the cards, to prevent you from tampering with the cards you'd draw next.
After searching a card from your Deck, by an effect, you must shuffle your Deck afterwards, unless the card's effect says otherwise. Similarly after returning a card(s) to their Deck(s), players must also shuffle it, unless stated otherwise.
Some card effects do not involve searching your Deck but do involve shuffling it.
Older card texts include the phrase "shuffle your Deck afterwards". However it was considered redundant, so newer texts omit the phrase.