softwareserial between arduino uno and esp8266

Make sure that:

1. RX pin on the Arduino UNO is connected to the TX pin on the ESP8266.
2. TX pin on the Arduino UNO is connected to the RX pin on the ESP8266.
3. Baud rate should be set to the same value from both the Arduino and ESP8266.

I don't know about your arduino but looking at this schematic, your RX and TX should be swapped.

Adding to the above answer. UNO's TX is at 5V , while ESP8266 's RX is at 3.3V, as it is a 3.3V module. So its better to use a resistive divider to bring UNO' TX to 3.3V and then feed to ESP's RX, instead of directly connecting them eachother.