That role falls to the sponsor to explain in a sponsor letter. There is no precise formulae guaranteeing success, but the object of a sponsor letter is to anticipate the decision-maker's questions and then to address as many as possible.
You can treat this list as something like "pick and choose" the items relevant to your specific situation...
- the sponsor's status in the host country (commonly citizen)
- the sponsor's job, career, or occupation
- the sponsor's relationship to the applicant (important)
- motivation for sponsorship (extremely important)
- sponsor's history of previous sponsorship with other applicants (important)
- how and where you first met (important)
- how you stay in touch between visits (important if visits are sporadic)
- the history of visits to one and other (important)
- how the visits have been financed
- why a visit is contemplated at this particular time (extremely important)
- time span and locale(s) for the visit
- the activities of the visit (commonly to maintain relationships, or a trial relationship)
- if the applicant and sponsor are both adults but in different generations then an explanation (very important)
- accommodation arrangements, along with proof of capacity to offer accommodation (very important)
- maintenance arrangements, along with proof of capacity to offer maintenance (very important)
- confirmation that the sponsor and applicant share a common language (extremely important if any doubt exists)
- confirmation of that the sponsor will be at the arrivals hall
- confirmation that the sponsor will be in residence for the entire duration of the visit
Nobody will do every one of these, but successful sponsors will be sure that the main points are covered.
The sponsorship letter is a voluntary step! There is no statutory requirement to include one and not including one will not bring about an automatic refusal.
Note that the sponsor stays in their "own box". They do not attempt to explain the applicant's personal circumstances or make attestations that are outside of their control (like absconding or overstaying). Doing this can cause credibility problems.
If you think some of these items are none of their business or are too embarrassing to explain, that usually means those things need to be explained more aggressively and in even greater depth and transparency.
Generally the letter is sent directly to the consulate with a marked copy sent to the applicant (who includes it in their bundle). The subject line of the letter is applicant's full name, date of birth, and nationality. The letter does not need to be certified or notarised or 'made official' in some other way.
Caveat: this answer does not address the situation where boyfriends and girlfriends are meeting for the first time following a prelude of email and Skype correspondence. Those situations are more desultory and better suited as a stand-alone question/answer.
Caveat: this list does not address the various considerations if children are among the applicants. Some of the letter would need to take up statutory requirements. Perhaps that's a future question.
Related: What should a sponsor tell the ECO?
Related: Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not reliable