The runners are how the plants propagate themselves. Depending on variety, the mother plants are only productive for a couple of seasons and need to be replaced. Cultivating some of the runners is vital to the maintenance of the strawberry patch. They are the replacements for the mother plants when they become too old to be productive.

It's important to know what kind of strawberries you have as June bearing are treated differently from day neutral or everbearing types.

Here is a link that might be useful: this link may help

Depends. If you just planted those strawberries then you would want to clip any runners those plant produce off this year so those plants can grow and produce fruit. However, once they do fruit then the runners should be left to propagate, produce new plants for the following years.
Perhaps this article from the University of Illinois might be helpful.

Here is a link that might be useful: growing strawberries

I always cut off my runners and potted them up for new plants. I grow mine in window boxes. They've done well for 3 years now.

I let my June bearers make some runners and daughter plants the FIRST year. This is normal. You help place these runners so they are 6 or 7 inches apart .

^^^^ What Wayne does is the way I remember it.

Your strawberry beds will have several generations of plants.

A - Geezers. 4-5 years end of life, pull at the end of the season
B - Mature 2-years and up, heavy producing, tend to produce fewer runners.
C - Yearlings - low producing, lots of runners.
D - Babies from runners.
(age varies depending on variety and your growing conditions)

Sooooo ... You systematically encourage runners from the yearlings into the spots occupied by geezers and snip the rest. If you remove all but a couple of runners, the plant tends to put its energy into them. If you clip all the runners it produced lots more.

The mature ones and geezers - clip off the runners so it will make larger berry crop (unless it's a variety that produces heavily from 1st year runners). If you spot a low-producing old plant, remove it.

By the end of the picking season, you should have well-established babies. Slice out the geezers (low-producing or weak-looking) to make room for the new ones. Remove any that are crowding each other.

Next season ... last years babies will make replacements, last year's yearlings should be in full production, and you remove the aging ones.

My childhood neighbor had this down to an art: She had close-spaced rows and the generations sort of rotated and migrated back and forth as she got the new ones going and left areas fallow. She always left one row next to the fence, because she and my dad had an agreement ... we could eat anything in her garden we could reach through the fence, and he'd keep us from climbing it.