Campfires can blow embers into new areas that start a fire.

Or people who are burning rubbish on their property, etc

Discarded cigarettes butts

Sparks from machinery, trains breaking, etc

Electrical arcs (e.g. if a power line gets blown down or shorts out in strong winds)

Arson

If you have a bunch of flammable stuff in a pile and the ideal conditions for a fire to start and grow it doesn't take much

Edit to add: The lightening also doesn't need to be the typical lightening most people would associate with also having a thunderstorm attached to it. There's also "dry lightening" which doesn't need rain to happen. (I can't really ELI5 what causes dry lightening because I don't fully understand it myself)

The strong winds themselves don't "cause" the wildfires - the fires still need an ignition source like lightening, etc to start

But strong winds create the ideal conditions for fires to both start and to spread

Firstly they will result in fuel (stuff that can burn) accumulating. It will blow leaves off trees, grass around, etc and often this will clump in particular places (e.g. around the bases of trees) and a big pile of flammable material is much more likely to catch fire and the fire will get intense quicker than if it is more spread out.

The wind also assists in drying out this fuel. The winds can carry away water vapor which results in stuff drying out quicker. And dry stuff burns better than wet stuff

Once the fire starts it also greatly helps in spreading the fire by blowing the flames in the direction of the wind giving them quicker and better access to more stuff that can burn.

More air also means oxygen going into a fire which allows the fire to burn more intensely (ever blown on a camp fire to help it get going?)

The strong winds will also pick up stuff that is still hot/burning from the main fire front and blow it to new areas and if these bits happen to land on something else that is flammable it can cause a new fire to start.