A basic, not overly-long, text message is sent using SMS (= Short Message Service). Long text messages, or messages with attachments, are sent using MMS (= Multimedia Message Service).
If, say, you're using 'bundles' (of calls, texts and data) from your phone service provider, you'll get a certain number (or possibly an unlimited number) of SMS texts included in the package. However MMS text messages aren't included unless, as well as your 'bundle credit', you've also got some 'ordinary credit' on your phone account as well.
There are other reasons why MMS messages might not get through, even though SMS ones work fine, such as the relevant settings to access your phone company's MMS server not being properly configured on your phone.
A call to your phone service provider can usually sort such any problems out, although you'll need to have your debit card handy if the problem relates to having no 'ordinary credit' available for you to use.