To build on these good answers, a large part of Charles II’s apparent popularity was the unpopularity of the Protectorate preceding him.

England had been fairly evenly split politically between Royalists and Roundheads in the civil wars only a decade or two before, but a much more significant split at this time, and one that had been brewing since Elizabeth’s reign, was the religious divide in the country.

There are too many players to recount in detail here, from crypto-Catholics and outright wacky sects (eg the Levellers), but the biggest opposed forces were those of the High Church and the Godly (aka Puritans). Nb these are loose terms just used for ease.

Puritan pressure to enforce ascetic Protestant mores on England had been present since Edward’s short reign, but the Elizabethan settlement (and the length of her reign) had kept a lid on this. This was upset by the Stuart monarchs’ more relaxed view of the church as an entity promoting the majesty of the crown and promoting a more mystical view of religion that left less room for political dissent against the head of the church (the king). This started with James I, a monarch more inclined to autocracy than Elizabeth and interested in any intellectual and theological justifications for it (eg Basilikon Doron, and the Book of Sports which encouraged Maypole dancing) but really gains pace with Archbishop Laud’s reforms in the reign of Charles.

Theologically, these repudiated the doctrine of predestination, a core plank of Calvinist thought, which many saw as a key differentiator from Catholic thinking (despite some Protestants countenancing it, eg Arminians) but aesthetically, they moved the Anglican Church toward a more ornate look. From a High Church perspective, these were efforts to standardise the Anglican communion, but also to emphasise the mysticism and majesty of the Church.

To many Puritans, though, this looked like an effort to reintroduce Catholicism into the Church through the back door. Especially unpopular here were Laud’s meddling with the communion tables of churches, to resemble catholic altars.

Against this backdrop, by the 1640s the High Church was indelibly associated with the King (as the ultimate sponsor of Laud’s reforms) and the Puritans with Parliament, with many leading Roundhead MPs from the South East coming from this background, eg Cromwell.

Long story short, Parliament won the civil wars, but along the way purged its more squeamish members.

The remaining Parliamentarians (and later Cromwell) had no qualms about imposing Puritan mores on he entire population during the interregnum.

The problem here is that these mores were not necessarily very fun: Christmas celebrations were repeatedly banned, dancing was curtailed and many pubs and inns were closed. Most famously, one of the first acts of the rebelling parliament in 1642 was to ban theatres on religious grounds:

“Public Stage-Plays shall cease and be forborne, instead of which are recommended to the People of this land the profitable and seasonable considerations of Repentance, Reconciliation and Peace with God, which probably may produce outward Peace and Prosperity, and bring again Times of Joy and Gladness to this Nation.”

Recent historiography has cast some doubt on how strongly these bans were enforced (and some artists continue to work in some fashion, eg Davenant) but bearing in mind this is just a few decades after the Golden Age of English theatre, of Shakespeare and Marlowe, the interregnum was a big step back for having fun in England for anyone who was not personally a Puritan.

Charles II was obviously aware of this reputation for grey joylessness which the Roundheads acquired, and immediately lifted many of these bans on his return, and recommenced the royal tradition of lavish patronage for artists and creative types. It was easy to spin this as the return to a mythical golden age of “Merrie England” , where the people returned to their joyful natural state of dancing, festivity and love of their king.

How true this affection was is hard to quantify - there were a lot of bitter Roundheads pining for the Good Old Cause for years to come, but after such a bleak few decades where fun was hard to come by, it is easy to imagine a Restoration, emphasising a return to both the natural order of monarchy and to beloved and joyous traditions, being greeted very warmly indeed by a people tired by two decades of war, religious strife and of life in Gilead.