Compile Visual Studio program with database and move to another PC

Just a basic question, when making a form with database in visual studio and after compiling is it necessary the computer where I will pass the files to run have sql installed or can I run the good program without any errors? I ask therefore when doing a test in another PC passing the compilation files to run in another PC it appears an error of network the instance when establishing connection with the SQL Server. However while continuing the program runs and writes to the database of good because in the compilation files there are 2 files of the bank one with extension mdf and ldf, I do not know if something can happen in the future or how I can do to execute and ignore this error so that does not appear anymore?