Wikipedia (https://en.wikipedia.org/wiki/Święconka) offers this explanation:

Baskets containing a sampling of Easter foods are brought to church to be blessed on Holy Saturday. The basket is traditionally lined with a white linen or lace napkin and decorated with sprigs of boxwood (bukszpan), the typical Easter evergreen.  Poles take special pride in preparing a decorative and tasteful basket with crisp linens, occasionally embroidered for the occasion, and boxwood and ribbon woven through the handle.  Observing the creativity of other parishioners is one of the special joys of the event.

While in some older or rural communities, the priest visits the home to bless the foods, the vast majority of Poles and Polish Americans visit the church on Holy Saturday, praying at the Tomb of the Lord (the fourteenth and final Station of the Cross).  The Blessing of the Food is, however, a festive occasion.  The three-part blessing prayers specifically address the various contents of the baskets, with special prayers for the meats, eggs, cakes and breads.  The priest or deacon then sprinkles the individual baskets with holy water.

Modern ceremony in Poland

More traditional Polish churches use a straw brush for aspersing the water; others use the more modern metal holy water sprinkling wand.  In some parishes, the baskets are lined up on long tables; in others, parishioners process to the front of the altar carrying their baskets, as if in a Communion line.  Older generations of Polish Americans, descended from early 19th century immigrants, tend to bless whole meal quantities, often brought to church halls or cafeterias in large hampers and picnic baskets.

The foods in the baskets have a symbolic meaning:

Eggs - symbolise life and Christ's resurrection
Bread - symbolic of Jesus
Lamb - represents Christ
Salt - represents purification
Horseradish - symbolic of the bitter sacrifice of Christ
Ham - symbolic of great joy and abundance.

The food blessed in the church remains untouched according to local traditions until either Saturday afternoon or Sunday morning.

Beginning at 9am, the church still bare
from the celebration of the Lord's Passion,
we see the stages of preparation which
transform the church during
Holy Saturday:

The creation of the floral arrangements,
the final rehearsal with the candidates for
Baptism and Reception into the church,
the decoration of the Sanctuary
and dressing of the Altar,
the restoration of the statue of Our Lady.

Then in the evening we see the musicians
gather, and the congregation assemble, in
anticipation of the Easter Vigil.

With the fire already burning outside, the
people leave the church, followed by the
procession of servers,
Deacon Stephen Sharpe and Fr. Alan.

The church is darkened, to be illuminated
next by the New Light from the
Paschal Candle, carried aloft by
Deacon Stephen.