。
Small bakeries have been overwhelmed by supermarkets.
Literal
Small-scale bread-shops [topic-は] supermarket [by-に] were-overwhelmed.
圧倒される is the passive of 圧倒する ('to overwhelm, dominate'). The agent marker に ('by supermarkets') is standard passive-agent marking. パン屋 ('bread shop, bakery') — パン from Portuguese 'pão' (one of Japanese's oldest loanwords) + 屋 (shop suffix). スーパーマーケット is often shortened to スーパー.